Metabolite power calculation

power calculation
Author

Gibran Hemani and Nic Timpson

Published

January 26, 2023

Background

Sample of individuals who have had heart surgery, followed up and some number go on to have kidney disease. What is the predictive rsq of a metabolite on kidney disease outcome, that has 80% power to be detected after multiple testing correction?

Simulation

Call libraries

library(fmsb)
library(dplyr)

Attaching package: 'dplyr'
The following objects are masked from 'package:stats':

    filter, lag
The following objects are masked from 'package:base':

    intersect, setdiff, setequal, union
library(ggplot2)

Define model

sim <- function(ncase, ncontrol, b)
{
  met <- rnorm(ncase+ncontrol)
  y <- rbinom(ncase+ncontrol, 1, plogis(log(ncase/(ncase+ncontrol)) + met*b + rnorm(ncase+ncontrol)))
  table(y)
  mod <- glm(y ~ met)
  rsq <- NagelkerkeR2(mod)$R2
  pval <- summary(mod)$coef[2,4]
  return(tibble(rsq, pval, ncase, ncontrol, b))
}

Set parameters

# Parameters
ntest <- 1500
ncase <- 70
ncontrol <- 100

Run

param <- expand.grid(
  b = seq(0, 1.5, by=0.01),
  sim = 1:100
)
res <- lapply(1:nrow(param), function(i) {
  sim(ncase=ncase, ncontrol=ncontrol, b=param$b[i])
}) %>% bind_rows()

Visualise

res %>% group_by(b) %>%
  summarise(rsq=mean(rsq), psig = sum(pval < (0.05/ntest))/n()) %>%
  ggplot(., aes(x=rsq, y=psig)) +
  geom_point() +
  geom_hline(yintercept=0.8) +
  labs(x="Negelkerke R2", y="Power", title=paste0(ncase, " cases, ", ncontrol, " controls, ", ntest, " independent tests"))

sessionInfo()
R version 4.2.1 Patched (2022-09-06 r82817)
Platform: aarch64-apple-darwin20 (64-bit)
Running under: macOS Monterey 12.6.2

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.2-arm64/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.2-arm64/Resources/lib/libRlapack.dylib

locale:
[1] en_GB.UTF-8/en_GB.UTF-8/en_GB.UTF-8/C/en_GB.UTF-8/en_GB.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] ggplot2_3.4.0 dplyr_1.0.10  fmsb_0.7.5   

loaded via a namespace (and not attached):
 [1] knitr_1.41        magrittr_2.0.3    munsell_0.5.0     tidyselect_1.2.0 
 [5] colorspace_2.0-3  R6_2.5.1          rlang_1.0.6       fastmap_1.1.0    
 [9] fansi_1.0.3       stringr_1.5.0     tools_4.2.1       grid_4.2.1       
[13] gtable_0.3.1      xfun_0.36         utf8_1.2.2        DBI_1.1.3        
[17] cli_3.5.0         withr_2.5.0       htmltools_0.5.4   assertthat_0.2.1 
[21] yaml_2.3.6        digest_0.6.31     tibble_3.1.8      lifecycle_1.0.3  
[25] farver_2.1.1      htmlwidgets_1.5.4 vctrs_0.5.1       glue_1.6.2       
[29] evaluate_0.19     rmarkdown_2.16    labeling_0.4.2    stringi_1.7.8    
[33] compiler_4.2.1    pillar_1.8.1      scales_1.2.1      generics_0.1.3   
[37] jsonlite_1.8.4    pkgconfig_2.0.3